Zone is very often apart of a power running game (see most NFL teams). Even the 1980's Redskins who popularized the counter/power play ran a lot of zone as well. They called their inside zone play Gut and it was their Base running play. Many times people think zone is only run by spread teams and is more of a finese run play but thats not always true. There are some great OL dvd's out there from Joe Bugel on the counter game, Russ Grimm on the power game and organizing the run game and Alex Gibbs on the inside and outside zone play. The Bugel and Gibbs tapes I think you can get on Gilman Gear and the Grimm tapes the Cool Clinic. The Bugel counter tape starts by talking about their base zone play and shows a clip of them blowing the 85 bears defense off the ball 5 yards with their zone combos.
So I think you will see some zone as well as power/counter. Most power running teams have the following plays in there playbook and run them out of mutiple formations:
Inside Zone strong/weak
Outside Zone strong/weak
Power strong/weak (fb/h kickout, backside guard lead through)
Counter strong/weak (backside guard kickout, fb/h/t/te pull through)
Then all sorts of variations off these too, whether they are blocking variations or misdirection plays. And play action passes off all them too.